Field Models in Electricity and Magnetism

ISBN-13: 9789048177356 / Angielski / Miękka / 2010 / 174 str.

Paolo Di Barba;Antonio Savini;Slawomir Wiak

Opis

The subject of computation in electricity and magnetism has so advanced in the past 40 years, since the advent of digital computers and thanks to the development of numerical methods, that today it urges and deserves adequate collocation also in curricula for electrical engineering. However, the time allotted to the subject in generalisnotverylargeinundergraduatestudies, wheremoreemphasisisstillusually attributed to circuits and systems than to ?elds. Moreover, ?eld models are generally not very popular among students, who are by far more familiar with circuit models. Even if one considers the quasi-static case, however, not only is electromagnetism fundamentalforpeopledealingwithelectricandmagneticdevices, butitprovidesthe basisfor, e.g.semiconductordevicedesign, bioengineeringapplicationsandsoforth. In the authors opinion, therefore, time has come to present ?eld models in el- tricity and magnetism, in the frame of an introductory textbook to be used by senior undergraduateorgraduatestudentsintheareaofelectricalandcomputerengineering. Elementary electromagnetism, basic vector analysis and fundamentals of numerical analysis are assumed to be known subjects. Havingthisinmind, theauthorshavecollectedtheexperiencetheyhaveaccu- lated in teaching electromagnetic theory at various levels and in different countries; theyintendtoofferabookonappliedelectricityandmagnetism, describingthepr- lemsofcalculatingelectromagnetic?eldsandtheintegralparametersconnectedwith them in suf?ciently clear and short form. The aim is that of writing a textbook containing the necessary background, i.e. laws explaining electromagnetic phenomena, mathematical operators and equations as well as methods for electromagnetic ?eld calculation. The latter include both analytical and numerical methods applied to the analysis as well as to the synthesis of electromagnetic devic

Spis treści

1 Introduction.

2 Vector fields. 2.1 Basic operators and equations. 2.2 Electrostatic field. 2.3 Magnetostatic field. 2.4 Steady conduction field.

3 Analytical methods for solving boundary-value problems. 3.1 Method of Green’s functions. 3.2 Method of images. 3.3 Method of separation of variables.

4 Numerical methods for solving boundary-value problems. 4.1 Variational formulation in magnetostatics. 4.2 Finite elements for two-dimensional magnetostatics. 4.3 Finite elements for three-dimensional magnetostatics.

5 Time-varying electromagnetic field. 5.1 Maxwell’s equations in differential form. 5.2 Poynting’s vector. 5.3 Maxwell’s equations in frequency domain. 5.4 Plane waves in an infinite domain. 5.5 Wave and diffusion equations in terms of vectors E and H. 5.6 Wave and diffusion equations in terms of scalar and vector potentials. 5.7 Electromagnetic field radiated by an oscillating dipole. 5.8 Diffusion equations in terms of dual potentials. 5.9 Weak eddy current in a conducting plane under a.c. conditions. 5.10 Strong eddy current in a conducting plane under a.c. conditions. 5.11 Eddy current in a cylindrical conductor under step excitation current. 5.12 Electromagnetic field equations in different reference frames.

6 Inverse problems. 6.1 Direct and inverse problems. 6.2 Well-posed and ill-posed problems. 6.3 Fredholm’s integral equation of the first kind. 6.4 Case study: synthesis of magnetic field sources. 6.5 Under- and over-determined systems of equations. 6.6 Least-squares solution. 6.7 Classification of inverse problems.

7 Optimization. 7.1 Solution of inverse problems by the minimization of a functional. 7.2 Constrained optimization. 7.3 Multiobjective optimization. 7.4 Gradient–free and gradient-based methods. 7.5 Deterministic vs non-deterministic search. 7.6 A deterministic algorithm of lowest order: simplex method. 7.7 A non-deterministic algorithm of lowest order: evolution strategy. 7.8 Numerical case studies.

8 Conclusion.

References. Acknowledgements. APPENDIX.

Blurb

Covering the development of field computation in the past forty years, Field Models in Electricity and Magnetism intends to be a concise, comprehensive and up-to-date introduction to field models in electricity and magnetism, ranging from basic theory to numerical applications.

The approach assumed throughout the whole book is to solve field problems directly from partial differential equations in terms of vector quantities.

Theoretical issues are illustrated by practical examples. In particular, a single example is solved by different methods so that, by comparison of results, limitations and advantages of the various methods are made clear.

The subjects of the synthesis of fields and of the optimal design of devices, which are growing in research and so far have not been adequately covered in textbooks, are developed in addition to more classical subjects of analysis.

Topics covered include:

• vector fields: electrostatics, magnetostatics, steady conduction;
• analytical methods for solving boundary-value problems;
• numerical methods for solving boundary-value problems;
• time-varying electromagnetic field;
• inverse problems;
• optimization.

Field Models in Electricity and Magnetism results from the cooperation of three authors in teaching electromagnetic theory at various levels and in different countries.